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Function in q-analog theory
In q-analog theory, the q {\displaystyle q} -gamma function, or basic gamma function, is a generalization of the ordinary gamma function closely related
Q-gamma_function
Extension of the factorial function
the gamma function (represented by Γ {\displaystyle \Gamma } , capital Greek letter gamma) is the most common extension of the factorial function to
Gamma_function
Generalization of the Euler gamma function and the Barnes G-function
gamma function Γ N {\displaystyle \Gamma _{N}} is a generalization of the Euler gamma function and the Barnes G-function. The double gamma function was
Multiple_gamma_function
Types of special mathematical functions
In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems
Incomplete_gamma_function
Special functions of several complex variables
function – and thus the others too – is intimately connected to the Jackson q-gamma function via the relation ( Γ q 2 ( x ) Γ q 2 ( 1 − x ) ) − 1 = q
Theta_function
Mathematic function
the elliptic gamma function is a generalization of the q-gamma function, which is itself the q-analog of the ordinary gamma function. It is closely
Elliptic_gamma_function
Statistics function
statistics, the Q-function is the tail distribution function of the standard normal distribution. In other words, Q ( x ) {\displaystyle Q(x)} is the probability
Q-function
Probability distribution
{\gamma (\alpha ,\beta x)}{\Gamma (\alpha )}},} where γ ( α , β x ) {\displaystyle \gamma (\alpha ,\beta x)} is the lower incomplete gamma function. If
Gamma_distribution
Model-free reinforcement learning algorithm
given infinite exploration time and a partly random policy. "Q" refers to the function that the algorithm computes: the expected reward—that is, the
Q-learning
Meromorphic function on the complex plane
the Riemann zeta function: γ ( Q , s ) = π − s 2 Γ ( s 2 ) . {\displaystyle \gamma (\mathbb {Q} ,s)=\pi ^{-{\frac {s}{2}}}\,\Gamma \left({\frac {s}{2}}\right)
L-function
Two-parameter family of continuous probability distributions
denominator is the gamma function. Many math packages allow direct computation of Q {\displaystyle Q} , the regularized gamma function. Provided that α
Inverse-gamma_distribution
Extension of the factorial function
Hadamard's gamma function, named after Jacques Hadamard, is an extension of the factorial function, different from the classical gamma function (it is an
Hadamard's_gamma_function
Result on gamma function
subsequently been found. The theorem also generalizes to the q {\displaystyle q} -gamma function. For every n ∈ N 0 , {\displaystyle n\in \mathbb {N} _{0}
Hölder's_theorem
Mathematical constants
The gamma function is an important special function in mathematics. Its particular values can be expressed in closed form for integer, half-integer, and
Particular values of the gamma function
Particular_values_of_the_gamma_function
Mathematical function
In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: ψ ( z ) = d d z ln Γ ( z ) = Γ ′ ( z ) Γ ( z )
Digamma_function
Concept in combinatorics (part of mathematics)
also obtains a q-analog of the gamma function, called the q-gamma function, and defined as Γ q ( x ) = ( 1 − q ) 1 − x ( q ; q ) ∞ ( q x ; q ) ∞ {\displaystyle
Q-Pochhammer_symbol
Difference between logarithm and harmonic series
gcd(a,q) = d then q γ ( a , q ) = q d γ ( a d , q d ) − log d . {\displaystyle q\gamma (a,q)={\frac {q}{d}}\gamma \left({\frac {a}{d}},{\frac {q}{d}}\right)-\log
Euler's_constant
Elliptic gamma function Hahn–Exton q-Bessel function Jackson q-Bessel function q-exponential q-gamma function q-theta function Lists of mathematics topics
List_of_q-analogs
Function in statistics
The generalized Marcum Q function of order ν > 0 {\displaystyle \nu >0} can be represented using incomplete Gamma function as Q ν ( a , b ) = 1 − e − a
Marcum_Q-function
Function for Heun's differential equation
In mathematics, the local Heun function H ℓ ( a , q ; α , β , γ , δ ; z ) {\displaystyle H\ell (a,q;\alpha ,\beta ,\gamma ,\delta ;z)} is the solution of
Heun_function
Function defined by a hypergeometric series
non-negative integer, one has 2F1(z) → ∞. Dividing by the value Γ(c) of the gamma function, we have the limit: lim c → − m 2 F 1 ( a , b ; c ; z ) Γ ( c ) = (
Hypergeometric_function
Meromorphic function
\mathbb {C} } defined as the (m + 1)th derivative of the logarithm of the gamma function: ψ ( m ) ( z ) := d m d z m ψ ( z ) = d m + 1 d z m + 1 ln Γ ( z )
Polygamma_function
Q-analog of hypergeometric series
hypergeometric series 2 ϕ 1 ( q α , q β ; q γ ; q , x ) {\displaystyle {}_{2}\phi _{1}(q^{\alpha },q^{\beta };q^{\gamma };q,x)} was first considered by
Basic_hypergeometric_series
The Stone–Geary utility function takes the form U = ∏ i ( q i − γ i ) β i {\displaystyle U=\prod _{i}(q_{i}-\gamma _{i})^{\beta _{i}}} where U {\displaystyle
Stone–Geary_utility_function
Mathematical function
mathematics, particularly q-analog theory, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general
Ramanujan_theta_function
Special function in mathematics
zeta function has an integral representation ζ ( s , a ) = 1 Γ ( s ) ∫ 0 ∞ x s − 1 e − a x 1 − e − x d x {\displaystyle \zeta (s,a)={\frac {1}{\Gamma (s)}}\int
Hurwitz_zeta_function
Generalization of the Meijer G-function and the Fox–Wright function
B_{2})&\ldots &(b_{q},B_{q})\end{matrix}}\right.\right]={\frac {1}{2\pi i}}\int _{L}{\frac {\prod _{j=1}^{m}\Gamma (b_{j}+B_{j}s)\,\prod _{j=1}^{n}\Gamma (1-a_{j}-A_{j}s)}{\prod
Fox_H-function
Probability distribution
distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution f ( x ; x 0 , γ ) {\displaystyle f(x;x_{0},\gamma )} is the distribution
Cauchy_distribution
Statistical function that defines the quantiles of a probability distribution
{\mathcal {D}}} is the function Q {\displaystyle Q} such that Pr [ X ≤ Q ( p ) ] = p {\displaystyle \Pr \left[\mathrm {X} \leq Q(p)\right]=p} for any random
Quantile_function
Type of mathematical function
^{s-1}q^{1/2-s}\sin \left({\frac {\pi }{2}}(s+\delta )\right)\Gamma (1-s)L(1-s,{\overline {\chi }}),} where Γ {\displaystyle \Gamma } is the gamma function
Dirichlet_L-function
Mathematical function
the Euler function is given by ϕ ( q ) = ∏ k = 1 ∞ ( 1 − q k ) , | q | < 1. {\displaystyle \phi (q)=\prod _{k=1}^{\infty }(1-q^{k}),\quad |q|<1.} Named
Euler_function
Arithmetic function related to the divisors of an integer
involving the divisor function is: ∑ n = 1 ∞ q n σ a ( n ) = ∑ n = 1 ∞ ∑ j = 1 ∞ n a q j n = ∑ n = 1 ∞ n a q n 1 − q n = ∑ n = 1 ∞ Li − a ( q n ) {\displaystyle
Divisor_function
Extension of superfactorials to the complex numbers
Barnes G-function G ( z ) {\displaystyle G(z)} is a function that is an extension of superfactorials to the complex numbers. It is related to the gamma function
Barnes_G-function
Analytic function that does not satisfy a polynomial equation
logarithm and inverse trigonometric functions. All special functions such as the gamma, error, bessel, and Riemann zeta functions are transcendental. Equations
Transcendental_function
Family of power series in mathematics
Gamma function as p F q ( a 1 , … , a p ; b 1 , … , b q ; z ) = ∑ n = 0 ∞ ( a 1 ) n ⋯ ( a p ) n ( b 1 ) n ⋯ ( b q ) n z n n ! = Γ ( b 1 ) ⋯ Γ ( b q )
Generalized hypergeometric function
Generalized_hypergeometric_function
Mathematical function
trigamma function but the circular functions are replaced by Clausen's function. Namely, ψ 1 ( p q ) = π 2 2 sin 2 ( π p / q ) + 2 q ∑ m = 1 ( q − 1 )
Trigamma_function
Analytic function on the upper half-plane with a certain behavior under the modular group
the function γ ( z ) = ( a z + b ) / ( c z + d ) {\textstyle \gamma (z)=(az+b)/(cz+d)} . The identification of functions with matrices makes function composition
Modular_form
Generalization of the hypergeometric function
(1-a_{j}+s)}{\prod _{j=m+1}^{q}\Gamma (1-b_{j}+s)\prod _{j=n+1}^{p}\Gamma (a_{j}-s)}}\,z^{s}\,ds,} where Γ denotes the gamma function. This integral is of the
Meijer_G-function
Family of solutions to related differential equations
_{m=0}^{\infty }{\frac {(-1)^{m}}{m!\,\Gamma (m+\alpha +1)}}{\left({\frac {x}{2}}\right)}^{2m+\alpha },} where Γ(z) is the gamma function, a shifted generalization
Bessel_function
Probability distribution
Gamma (d/p)}},} where Γ ( ⋅ ) {\displaystyle \Gamma (\cdot )} denotes the gamma function. The cumulative distribution function is F ( x ; a
Generalized gamma distribution
Generalized_gamma_distribution
In mathematics, the p-adic gamma function Γp is a function of a p-adic variable analogous to the gamma function. It was first explicitly defined by Morita
P-adic_gamma_function
Concept in mathematics
generalization of the factorial to the gamma function. There are multiple equivalent definitions of the K-function. The direct definition: K ( z ) = ( 2
K-function
Mathematical function
Im(τ) > 0, let q = e2πiτ; then the eta function is defined by, η ( τ ) = e π i τ 12 ∏ n = 1 ∞ ( 1 − e 2 n π i τ ) = q 1 24 ∏ n = 1 ∞ ( 1 − q n ) . {\displaystyle
Dedekind_eta_function
which for this function simply equals r. Elasticity of demand is indicated by r = d Q d P P Q {\displaystyle {r}={\frac {dQ}{dP}}{\frac {P}{Q}}} , where r
Isoelastic_function
Probability distribution
V(x;\sigma ,\gamma )={\frac {\operatorname {Re} [w(z)]}{{\sqrt {2\pi }}\,\sigma }},} where Re[w(z)] is the real part of the Faddeeva function evaluated for
Voigt_profile
Function uniquely mapping two numbers into a single number
mathematics, a pairing function is a process to uniquely encode two natural numbers into a single natural number. Any pairing function can be used in set
Pairing_function
Analytic function in mathematics
{d} x} is the gamma function. The Riemann zeta function is defined for other complex values via analytic continuation of the function defined for σ >
Riemann_zeta_function
Identity obeyed by many special functions related to the gamma function
identity obeyed by many special functions related to the gamma function. For the explicit case of the gamma function, the identity is a product of values;
Multiplication_theorem
Ability of a body to store an electrical charge
charges Q 1 , Q 2 , Q 3 {\displaystyle Q_{1},Q_{2},Q_{3}} , then the voltage (actually potential) at conductor 1 is given by V 1 = P 11 Q 1 + P 12 Q 2 + P
Capacitance
Sigmoid shape special function
minimax approximation or bound for the closely related Q-function: Q(x) ≈ Q̃(x), Q(x) ≤ Q̃(x), or Q(x) ≥ Q̃(x) for x ≥ 0. The coefficients {(an,bn)}N n = 1 for
Error_function
Generalisation of the generalised hypergeometric function pFq(z)
(a_{p}+A_{p}n)}{\Gamma (b_{1}+B_{1}n)\cdots \Gamma (b_{q}+B_{q}n)}}\,{\frac {z^{n}}{n!}}} it becomes pFq(z) for A1...p = B1...q = 1. The Fox–Wright function is a
Fox–Wright_function
Continuous probability distribution
{\displaystyle \gamma _{2}={\frac {-6\Gamma _{1}^{4}+12\Gamma _{1}^{2}\Gamma _{2}-3\Gamma _{2}^{2}-4\Gamma _{1}\Gamma _{3}+\Gamma _{4}}{[\Gamma _{2}-\Gamma _{1}^{2}]^{2}}}}
Weibull_distribution
Function with unusual fractal properties
{\displaystyle \gamma \in M} as a general element of the monoid, there is a corresponding self-symmetry of the question mark function: γ D ∘ ? = ? ∘ γ
Minkowski's question-mark function
Minkowski's_question-mark_function
Formulation of classical mechanics
=\gamma (\tau ;t,t_{0},\mathbf {q} ,\mathbf {q} _{0})} into the action functional results in the Hamilton's principal function (HPF) S ( q , t ; q 0
Hamilton–Jacobi_equation
Probability distribution and special case of gamma distribution
incomplete gamma function and P ( s , t ) {\textstyle P(s,t)} is the regularized gamma function. In a special case of k = 2 {\displaystyle k=2} this function has
Chi-squared_distribution
Transcendental single-variable function
{\displaystyle 0<z<1} , the Clausen function of second order can be expressed in terms of the Barnes G-function and (Euler) Gamma function: Cl 2 ( 2 π z ) = 2 π
Clausen_function
Special mathematical function defined as sin(x)/x
}\left(1-{\frac {x^{2}}{n^{2}}}\right)} and is related to the gamma function Γ(x), as well as to Gauss' Pi function, through Euler's reflection formula: sin ( π x
Sinc_function
Solutions of Legendre's differential equation
terms of the hypergeometric function, 2 F 1 {\displaystyle _{2}F_{1}} . With Γ {\displaystyle \Gamma } being the gamma function, the first solution is P
Legendre_function
Probability distribution
density function (pdf): G B ( y ; a , b , c , p , q ) = | a | y a p − 1 ( 1 − ( 1 − c ) ( y / b ) a ) q − 1 b a p B ( p , q ) ( 1 + c ( y / b ) a ) p + q for
Generalized_beta_distribution
Number of integers coprime to and less than n
generating function is ∑ n = 1 ∞ φ ( n ) q n 1 − q n = q ( 1 − q ) 2 {\displaystyle \sum _{n=1}^{\infty }{\frac {\varphi (n)q^{n}}{1-q^{n}}}={\frac {q}{(1-q)^{2}}}}
Euler's_totient_function
Analyzes the topology of a manifold by studying differentiable functions on that manifold
Then M q + ε {\displaystyle M^{q+\varepsilon }} is homotopy equivalent to M q − ε {\displaystyle M^{q-\varepsilon }} with a γ {\displaystyle \gamma } -cell
Morse_theory
Model parameters in mathematical finance
derivatives: delta, vega, theta and rho; as well as gamma, a second-order derivative of the value function. The remaining sensitivities in this list are common
Greeks_(finance)
Probability distribution
{(k+r-1)(k+r-2)\dotsm (r)}{k!}}={\frac {\Gamma (k+r)}{k!\ \Gamma (r)}}=\left(\!\!{r \choose k}\!\!\right).} Note that Γ(r) is the Gamma function, and ( ( r k ) ) {\displaystyle
Negative binomial distribution
Negative_binomial_distribution
Mathematical function
incomplete gamma function. If Q ( a , z ) = Γ ( a , z ) Γ ( a ) = 1 Γ ( a ) ∫ z ∞ u a − 1 e − u d u {\displaystyle Q(a,z)={\frac {\Gamma (a,z)}{\Gamma (a)}}={\frac
Z_function
Probability distribution
{q\Gamma \left(\alpha +{\tfrac {1}{p}}\right)\Gamma (\beta -{\tfrac {1}{p}})}{\Gamma (\alpha )\Gamma (\beta )}}\quad {\text{if }}\beta p>1} and mode q
Beta_prime_distribution
Effective particle coupling beyond tree level
1 ( q 2 ) + i σ μ ν q ν 2 m F 2 ( q 2 ) {\displaystyle \Gamma ^{\mu }=\gamma ^{\mu }F_{1}(q^{2})+{\frac {i\sigma ^{\mu \nu }q_{\nu }}{2m}}F_{2}(q^{2})}
Vertex_function
Mathematical problem in cryptography
-vectors over Z q {\displaystyle \mathbb {Z} _{q}} . There exists a certain unknown linear function f : Z q n → Z q {\displaystyle f:\mathbb {Z} _{q}^{n}\rightarrow
Learning_with_errors
Discrete probability distribution
using the lgamma function in the C standard library (C99 version) or R, the gammaln function in MATLAB or SciPy, or the log_gamma function in Fortran 2008
Poisson_distribution
Special function defined by an integral
case of the upper incomplete gamma function: E n ( x ) = x n − 1 Γ ( 1 − n , x ) . {\displaystyle E_{n}(x)=x^{n-1}\Gamma (1-n,x).} The generalized form
Exponential_integral
Mathematical function
{(q^{a}+q^{2p-a})(q^{a+p}+q^{p-a})}{1-q^{3p}+{\cfrac {q^{p}(q^{a}+q^{3p-a})(q^{a+2p}+q^{p-a})}{1-q^{5p}+{\cfrac {q^{2p}(q^{a}+q^{4p-a})(q^{a+3p}+q
Jacobi_elliptic_functions
average value of 1 Q k {\displaystyle 1_{Q_{k}}} , denoted by δ ( n ) {\displaystyle \delta (n)} , in terms of the zeta function. The function δ {\displaystyle
Average order of an arithmetic function
Average_order_of_an_arithmetic_function
Function studied by Ramanujan
function, studied by Srinivasa Ramanujan, is the function τ : N → Z {\displaystyle \tau :\mathbb {N} \to \mathbb {Z} } defined by ∑ n = 1 ∞ τ ( n ) q
Ramanujan_tau_function
Existence and uniqueness of solutions to initial value problems
0\leq q<1,} such that ‖ Γ φ 1 − Γ φ 2 ‖ ∞ ≤ q ‖ φ 1 − φ 2 ‖ ∞ {\displaystyle \left\|\Gamma \varphi _{1}-\Gamma \varphi _{2}\right\|_{\infty }\leq q\left\|\varphi
Picard–Lindelöf_theorem
Modular function in mathematics
eta function η ( 2 i ) {\displaystyle \eta (2i)} has the exact value, η ( 2 i ) = Γ ( 1 4 ) 2 11 / 8 π 3 / 4 {\displaystyle \eta (2i)={\frac {\Gamma \left({\frac
J-invariant
Risk measure estimating the average loss in the worst tail of the distribution
}{1-\alpha }}\Gamma \left(1+{\frac {1}{k}},-\ln(1-\alpha )\right)} , where Γ ( s , x ) {\displaystyle \Gamma (s,x)} is the upper incomplete gamma function. If the
Expected_shortfall
Concept in probability
Γ ( t ; μ q , μ q 2 ν ) {\displaystyle X^{VG}(t;\sigma ,\nu ,\theta )\;:=\;\Gamma (t;\mu _{p},\mu _{p}^{2}\,\nu )-\Gamma (t;\mu _{q},\mu _{q}^{2}\,\nu
Variance_gamma_process
Generalization of the Riemann zeta function for algebraic number fields
that [ K : Q ] = r 1 + 2 r 2 {\displaystyle [K:\mathbb {Q} ]=r_{1}+2r_{2}} . In terms of the gamma function Γ ( s ) {\displaystyle \Gamma (s)} , define
Dedekind_zeta_function
Multiplicative function in number theory
^{2}n}{n}}=-2\gamma ,} where γ {\displaystyle \gamma } is Euler's constant. The Lambert series for the Möbius function is ∑ n = 1 ∞ μ ( n ) q n 1 − q n = q , {\displaystyle
Möbius_function
Distance function defined between probability distributions
\mu } into ν {\displaystyle \nu } can be described by a function γ ( x , y ) {\displaystyle \gamma (x,y)} which gives the amount of mass to move from x {\displaystyle
Wasserstein_metric
Method of solution to differential equations
integrals of Green's functions and sums of the same. For example, if L = ( ∂ x + γ ) ( ∂ x + α ) 2 {\displaystyle L=\left(\partial _{x}+\gamma \right)\left(\partial
Green's_function
z}}\left(e^{\gamma z}{\frac {\zeta (z+1,q)}{\Gamma (-z)}}\right),} where ψ(z) is the polygamma function and ζ(z,q), is the Hurwitz zeta function. The function is
Balanced_polygamma_function
/2}\cdot {\frac {{}_{2}F_{1}(v+1,-v;1-\mu ;1/2-x/2)}{\Gamma (1-\mu )}}} Ferrers function of the second kind Q v μ ( x ) = π 2 sin ( μ π ) ( cos ( μ π ) (
Ferrers_function
Type of automaton
transition function, mapping Q × ( Σ ∪ { ε } ) × Γ {\displaystyle Q\times (\Sigma \cup \{\varepsilon \})\times \Gamma } into finite subsets of Q × Γ ∗ {\displaystyle
Pushdown_automaton
Special function defined by an integral
∈ Q + {\displaystyle r\in \mathbb {Q} ^{+}} (where λ is the modular lambda function), then K(k) is expressible in closed form in terms of the gamma function
Elliptic_integral
Reinforcement learning algorithms
{\displaystyle V(s)} , the action-value Q-function Q ( s , a ) , {\displaystyle Q(s,a),} the advantage function A ( s , a ) {\displaystyle A(s,a)} , or
Actor-critic_algorithm
Polynomial function of degree 4
In algebra, a quartic function is a function of the form f ( x ) = a x 4 + b x 3 + c x 2 + d x + e , {\displaystyle f(x)=ax^{4}+bx^{3}+cx^{2}+dx+e,} where
Quartic_function
Total species diversity in a landscape
equation is q D γ = 1 ∑ i = 1 S p i p i q − 1 q − 1 . {\displaystyle {}^{q}\!D_{\gamma }={\frac {1}{\sqrt[{q-1}]{\sum _{i=1}^{S}p_{i}p_{i}^{q-1}}}}.} The
Gamma_diversity
Heavy-tail probability distribution
are given by: α = 2 − q q − 1 , λ = 1 λ q ( q − 1 ) . {\displaystyle \alpha ={{2-q} \over {q-1}},~\lambda ={1 \over \lambda _{q}(q-1)}.} The logarithm
Lomax_distribution
Generalization of Gaussian distribution
− q ) ( 3 − q ) 1 − q Γ ( 3 − q 2 ( 1 − q ) ) for − ∞ < q < 1 {\displaystyle C_{q}={{2{\sqrt {\pi }}\Gamma \left({1 \over 1-q}\right)} \over {(3-q){\sqrt
Q-Gaussian_distribution
Technique for the generative modeling of a continuous probability distribution
z=(x_{0},x_{1})} and q ( z ) = Γ ( π 0 , π 1 ) {\displaystyle q(z)=\Gamma (\pi _{0},\pi _{1})} , where Γ {\displaystyle \Gamma } is the optimal transport
Diffusion_model
Evaluates a line integral through a gradient field using the original scalar field
( p ) {\displaystyle \int _{\gamma }\nabla \varphi (\mathbf {r} )\cdot \mathrm {d} \mathbf {r} =\varphi \left(\mathbf {q} \right)-\varphi \left(\mathbf
Gradient_theorem
Gamma matrices for arbitrary Clifford algebras
correspond to taking d = N = 4 and p, q = 1, 3 or 3, 1. In higher (and lower) dimensions, one may define a group, the gamma group, behaving in the same fashion
Higher-dimensional gamma matrices
Higher-dimensional_gamma_matrices
Partial differential equations
\cos \gamma =\cos \theta \cos \theta '+\sin \theta \sin \theta '\cos(\varphi -\varphi ').} The free-space circular cylindrical Green's function (see below)
Green's function for the three-variable Laplace equation
Green's_function_for_the_three-variable_Laplace_equation
Mathematical model for sequential decision making under uncertainty
has): Q ( s , a ) = ∑ s ′ P a ( s , s ′ ) ( R a ( s , s ′ ) + γ V ( s ′ ) ) . {\displaystyle \ Q(s,a)=\sum _{s'}P_{a}(s,s')(R_{a}(s,s')+\gamma V(s'))
Markov_decision_process
Probability distribution in economics
G={\frac {\Gamma (p)\Gamma (2p+1/a)}{\Gamma (2p)\Gamma (p+1/a)}}-1,} where Γ ( ⋅ ) {\displaystyle \Gamma (\cdot )} is the gamma function. Note that this
Dagum_distribution
Polynomial sequence
{2^{q}(q+2j+1)!}{(q-1)!\Gamma (q+2j+2\alpha +1)}}&\sum _{i=0}^{j}{\frac {(2i+\alpha +1)\Gamma (2i+2\alpha +1)}{(2i+1)!(j-i)!}}\\&\times {\frac {\Gamma (q+j+i+\alpha
Gegenbauer_polynomials
Concept in probability theory
probability of success q {\displaystyle q} in [0,1]. This random variable will follow the binomial distribution, with a probability mass function of the form p
Conjugate_prior
_{r};\rho _{s};z)\equiv {}&{\frac {\Gamma (\alpha _{q+1})}{\prod _{k=1}^{q}\Gamma (\rho _{k}-\alpha _{k})}}\prod _{\mu =1}^{q}\int _{0}^{\infty }\lambda _{\mu
MacRobert_E_function
Probability distribution
+ q ) Γ ( β ) {\displaystyle \operatorname {E} [X^{p}Y^{q}]=\operatorname {E} [X^{p}]\;\operatorname {E} [Y^{q}]={\frac {\Gamma (\alpha +p)}{\Gamma (\alpha
Distribution of the product of two random variables
Distribution_of_the_product_of_two_random_variables
{\displaystyle i\in \Gamma (y)} , a function A ( f , i ) : A ( y , i ) → A ( x , Γ ( f ) ( i ) ) {\displaystyle A(f,i):A(y,i)\to A(x,\Gamma (f)(i))} . This
Semantics_of_type_theory
Q GAMMA-FUNCTION
Q GAMMA-FUNCTION
Girl/Female
African, American, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Irish, Italian, Jamaican, Latin
Jewel; Precious Stone; Gem
Boy/Male
Arabic
Two Bright Stars Near the Pole; Beta and Gama in Ursa Minor
Girl/Female
Tamil
Beautiful, A destiny
Girl/Female
Norse
Grandmother.
Girl/Female
French Latin Italian
Jewel.
Girl/Female
Gujarati, Hindu, Indian
The Soothing Voice
Girl/Female
Hindu, Indian, Kannada, Telugu
Beautiful; A Destiny
Girl/Female
Danish, Indian, Latin, Sanskrit, Swedish
Loveable; Desire
Girl/Female
Hebrew
Without flaw.
Surname or Lastname
English
English : variant of Game.English : from Anglo-Norman French gambon ‘ham’, a diminutive of gambe, Norman-Picard form of Old French jambe ‘leg’ (Late Latin gamba), hence probably a nickname for someone with some peculiarity of the legs or gait.
Girl/Female
Australian, French, Hebrew
Without Flaw; Palm Tree; Perfect
Surname or Lastname
German
German : East Frisian patronymic from the nursery name Mamme, linked to Middle High German mamme, memme ‘mother’s breast’ (Latin mamma).English (of Norman origin) : from the Old French personal name Maismon, Maimon, of unknown etymology.Indian (Kerala) : variant of Thomas among Kerala Christians, with the Tamil-Malayalam third person masculine singular suffix -n. It is only found as a personal name in Kerala, but in the U.S. has come to be used as a family name among Kerala Christians.
Female
English
Italian name GEMMA means "precious stone."
Girl/Female
Arabic, Indian, Kashmiri
Beautiful Sky
Boy/Male
Indian
Supreme god.
Boy/Male
Muslim
The provider
Boy/Male
African, British, English, Indian
Mother; God-like
Boy/Male
Indian
The provider
Surname or Lastname
English
English : topographic name for someone who lived by a gate or ‘hatch’ (especially one leading into a forest), northern Middle English heck (Old English hæcc), or a habitational name from Great Heck in North Yorkshire, which is named with this word. Compare Hatch.German : topographic name from Middle High German hecke, hegge ‘hedge’. This name is common in southern Germany and the Rhineland.Possibly an Americanized spelling of French Hec(q), a topographic name from Old French hec ‘gate’, ‘barrier’, ‘fence’ (compare 1), or a habitational name from a place named with this word.Shortened form of the Dutch surname van (den) Hecke, a habitational name from any of several places called ten Hekke in the Belgian provinces of East and West Flanders.
Female
English
Variant spelling of Italian Gemma, JEMMA means "precious stone."
Q GAMMA-FUNCTION
Q GAMMA-FUNCTION
Surname or Lastname
English
English : variant of Small.
Girl/Female
Muslim/Islamic
Prostrating to Allah
Girl/Female
Hindu
Smiling
Boy/Male
Indian, Punjabi, Sikh
Absorbed in Light of God
Girl/Female
Scandinavian
Hannah, meaning favor, grace.
Boy/Male
Hindu
Knowing of three Vedas
Male
English
English name coined by Sir Walter Scott for a character in his novel Ivanhoe, thought to possibly be a variant spelling of Anglo-Saxon Cerdic, CEDRIC means "war chief."Â
Boy/Male
Hindu
Beauteous, Beloved
Boy/Male
Indian, Sanskrit
Faultless
Male
English
Pet form of English Reuben, RUBE means "behold, a son!"Â
Q GAMMA-FUNCTION
Q GAMMA-FUNCTION
Q GAMMA-FUNCTION
Q GAMMA-FUNCTION
Q GAMMA-FUNCTION
n.
An abbes or spiritual mother.
n.
A child's name for mamma, mother.
n.
Mamma.
n.
The llama.
n.
The third letter (/, / = Eng. G) of the Greek alphabet.
n.
See Mamma.
pl.
of Gemma
pl.
of Mamma
n.
A glandular organ for secreting milk, characteristic of all mammals, but usually rudimentary in the male; a mammary gland; a breast; under; bag.
n.
A leaf bud, as distinguished from a flower bud.
n.
A bud spore; one of the small spores or buds in the reproduction of certain Protozoa, which separate one at a time from the parent cell.
a.
Belonging to, or resembling, gumma.
pl.
of Gumma
q.
Moving or causing motion; motory; active, as opposed to latent.
n.
The viola di gamba, now entirely disused.
a.
Having the form of a mamma (breast) or mammae.
n.
A viola da gamba.
n.
A kind of soft tumor, usually of syphilitic origin.
a.
Of or pertaining to a gumma.
n.
Mother; -- word of tenderness and familiarity.